Prospects of measuring the branching fraction of the Higgs boson decaying into muon pairs at the International Linear Collider

The prospects for measuring the branching fraction of $$H \rightarrow \mu ^{+} \mu ^{-}$$ at the International Linear Collider (ILC) have been evaluated based on a full detector simulation of the International Large Detector (ILD) concept, considering centre-of-mass energies ( $$\sqrt{s}$$ ) of 250 GeV and 500 GeV with two different beam polarisation configurations of $${\mathcal {P}} (e^{-}, e^{+}) = (-\,80{\%}, +\,30{\%})$$ and $$(+\,80{\%}, -\,30{\%})$$ . For both $$\sqrt{s}$$ cases, the two final states $$e^{+} e^{-} \rightarrow q\overline{q}H$$ and $$e^{+} e^{-} \rightarrow \nu \overline{\nu }H$$ have been analyzed. For integrated luminosities of 2 $$\hbox {ab}^{-1}$$ at $$\sqrt{s} =250$$ GeV and 4 $$\hbox {ab}^{-1}$$ at $$\sqrt{s} =500$$ GeV, the combined precision on the branching fraction of $$H \rightarrow \mu ^{+} \mu ^{-}$$ is estimated to be 17%. The impact of the transverse momentum resolution for this analysis is also studied.